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Algebra · Polynomial-Equations

Solve 2x^3 - 3x^2 - 11x + 6 = 0

2 x^{3} - 3 x^{2} - 11 x + 6 = 0

Step by step

  1. 2 x^{3} - 3 x^{2} - 11 x + 6 = 0

    Start from the equation as given.

  2. \left(x - 3\right) \left(x + 2\right) \left(2 x - 1\right) = 0

    Factor the polynomial (rational-root test + division).

  3. 2 x - 1 = 0 \;\Rightarrow\; \frac{1}{2}

    Set each factor equal to zero and solve it.

  4. x - 3 = 0 \;\Rightarrow\; 3

    Set each factor equal to zero and solve it.

  5. x + 2 = 0 \;\Rightarrow\; -2

    Set each factor equal to zero and solve it.

  6. x = \frac{1}{2} ,\; x = 3 ,\; x = -2

    All 3 roots.

Reveal the answer
x = \frac{1}{2} ,\; x = 3 ,\; x = -2